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Chapter 10: Q.10.61 (page 417)
The formula for the pooled variance, , is given on page 407 Show that, if the sample sizes, and , are equal, then is th mean of and .
If the sample sizes, and , are equal, then is the mean of and .
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Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired -test, the paired Wilcoxon signed-rank test, or neither of these tests if preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is
a. approximately normal.
b. highly skewed; the sample size is .
c. symmetric bimodal.
In the article "Sleep Apnea in Adults With Traumatic Brain Injury: A Preliminary Investigation" (Archives of Physical Medicine and Rehabilitation, Vol. 82, Issue 3, pp. 316321), J. Webster et al, investigated sleep-related breathing disorders in adults with traumatic brain injuries (TBI). The respiratory disturbance index (RDI), which is the number of apneic and hypopneic episodes per hour of sleep, was used as a measure of severity of sleep apnea. An RDI of 5 or more indicates sleep-related breathing disturbances. The RDIs for the females and males in the study are as follows.
Use the technology of your choice to answer the following questions. Explain your answers.
a. If you had to choose between the use of pooled-procedures and nonpooled -procedures here, which would you choose?
b. Is it reasonable to use the type of procedure that you selected in part (a)?
O. Ehimwenma and M. Tagbo, researchers in Nigeria, were interested in how the characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. They published their findings in the article "Determination of Normal Dimensions of the Spleen by Ultrasound in an Endemic Tropical Environment" (Nigerian Medical Journal, Vol. 52, No. 3, pp. 198-203). The researchers randomly sampled males and females in Nigeria. The mean and standard deviation of the spleen lengths for the males were and respectively, and those for the females were and , respectively. At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians?
Faculty Salaries. Suppose, for Example, you want to decide whether the mean salary of faculty in private institutions is less than the mean salary of faculty in public institutions. State the null and alternative hypotheses for that hypothesis test.
Refer to Exercise and determine aconfidence interval for the difference between the mean dopamine activities of psychotic and nonpsychotic patients.
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